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Shear-induced Electrokinetic Lift at Large Péclet Numbers

Published online by Cambridge University Press:  09 July 2012

O. Schnitzer ,
I. Frankel  and
E. Yariv
O. Schnitzer
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology Technion City, 32000, Israel
I. Frankel
Affiliation:
Department of Aerospace Engineering, Technion – Israel Institute of Technology Technion City, 32000, Israel
E. Yariv*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology Technion City, 32000, Israel
*
∗ Corresponding author. E-mail: udi@technion.ac.il
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Abstract

We analyze the problem of shear-induced electrokinetic lift on a particle freely suspended near a solid wall, subject to a homogeneous (simple) shear. To this end, we apply the large-Péclet-number generic scheme recently developed by Yariv et al. (J. Fluid Mech., Vol. 685, 2011, p. 306). For a force- and torque-free particle, the driving flow comprises three components, respectively describing (i) a particle translating parallel to the wall; (ii) a particle rotating with an angular velocity vector normal to the plane of shear; and (iiii) a stationary particle in a shear flow. Symmetry arguments reveal that the electro-viscous lift, normal to the wall, is contributed by Maxwell stresses accompanying the induced electric field, while electro-viscous drag and torque corrections, parallel to the wall, are contributed by the Newtonian stresses accompanying the induced flow. We focus upon the near-contact limit, where all electro-viscous contributions are dominated by the intense electric field in the narrow gap between the particle and the wall. This field is determined by the gap-region pressure distributions associated with the translational and rotational components of the driving Stokes flow, with the shear-component contribution directly affecting only higher-order terms. Owing to the similarity of the corresponding pressure distributions, the induced electric field for equal particle–wall zeta potentials is proportional to the sum of translation and rotation speeds. The electro-viscous loads result in induced particle velocities, normal and tangential to the wall, inversely proportional to the second power of particle–wall separation.

Keywords

electro-viscous forcesStokes flowssingular perturbations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 64 - 81
Copyright
© EDP Sciences, 2012

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